Your employer should cease you on Revenue with your final pay and your date of cessation. After that has been completed, your tax credits will automatically assign to the next employer. You can assign your tax credits & cut off manually to your new employer on "MyAccount" with Revenue but I have seen this cause problems as your employer needs to assign an employee ID for each and every employment (can have more than one employee ID for the same employer - for e.g. if you have weekly pay and monthly bonus), so it may not be picked up with a manual assignation but treated as a separate employment. Some of these teething problems may have been ironed out by now though.